# Influence of Weld Parameters on the Fatigue Life of Deck-Rib Welding Details in Orthotropic Steel Decks Based on the Improved Stress Integration Approach

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## Abstract

**:**

## 1. Introduction

## 2. Equivalent Structural Stress Approach

#### 2.1. Stress-Based Integration Equivalent Structural Stress Approach

#### 2.2. Master S-N Curve

## 3. Parameter Influence and Mesh Sensitivity of the Stress Integration Approach

#### 3.1. Influence of Parameters $\delta $ and $w$

#### 3.2. Mesh Sensitivity

## 4. Experimental Verification of the Master S-N Curve

## 5. Fatigue Life Calculation of Jiangyin Bridge Based on the Stress Integration Approach

#### 5.1. Multi-Scale Model of Jiangyin Bridge

#### 5.2. Fatigue Vehicle Load

#### 5.3. Stress Time–History Curve

#### 5.4. Fatigue Life Calculation of Jiangyin Bridge Based on the Stress Integration Approach

## 6. Influence of Weld Parameters on the Fatigue Life of Deck-Rib Welding Details in the OSD

#### 6.1. Influence of Weld Size on the Bridge Fatigue Life

^{2}.

#### 6.2. Grinding Treatment

#### 6.2.1. Influence of Grinding Types

#### 6.2.2. Influence of Grinding Radius

#### 6.3. Influence of the Weld Penetration Rate

## 7. Conclusions

- The stress integration approach for the 3D solid elements showed that the structural stress does not change significantly with the parameters $w$ (width of the isolated body) and $\delta $ (the distance between the crack propagation surface and the reference surface). In order to simplify the calculation, $\delta $ was set as 0, and $w$ can be set as the mesh size along the weld length direction.
- When the mesh size is no more than 0.5 times the deck thickness, the mesh insensitivity of the stress integration approach is obviously better than that of the extrapolation hot spot stress approach. The mesh size in the stress integration approach is recommended to be 0.25 times the deck thickness, and the calculation error is approximately 2%.
- The slope of the master S-N curve at high cycles ($N>{10}^{7}$) significantly affects the bridge fatigue life, and the slope ${m}_{2}=5$ at high cycles is more reasonable.
- The weld parameter analysis for Jiangyin Bridge showed the following: (1) The change of weld size caused by weld manufacturing errors can obviously affect the bridge fatigue life. The fatigue life of five different weld types varies from 51 years to 113 years under a standard vehicle load. The weld fatigue life increases with the decrease of the angle ${\alpha}_{2}$ between the deck and the rib and the increase of the weld area. (2) A new grinding treatment type that does not weaken the deck is proposed. It is more beneficial to improve the fatigue life of the deck-rib welding details, and the fatigue life increases by approximately 5% when the grinding radius increases by 2 mm. (3) The fatigue life with 80% partial penetration is slightly higher than that of 100% full penetration. (4) In practice, the most favorable weld type is WT-3 with an angle ${\alpha}_{2}$ of 30 degrees and an area of 48 mm
^{2}. The grinding type that does not weaken the deck is more conducive to improving the bridge fatigue life. The 80% partial penetration of the deck-rib welding details condition is recommended.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Variation of structural stress with the parameters $\delta $ and $w$. (

**a**) The parameter $\delta $ ($w=2$ mm). (

**b**) The parameter $w$ ($\delta =0$).

**Figure 16.**Moving vehicle in the FEM. (

**a**) Moving vehicle longitudinal distribution; (

**b**) Vehicle transverse distribution.

Statistical Basis | ${\mathit{C}}_{\mathit{s}}$ | h |
---|---|---|

Mean | 19,930.2 | −0.32 |

$+2\sigma \text{}(\mathrm{Upper}95)$ | 28,626.5 | |

$-2\sigma \text{}(\mathrm{Lower}95)$ | 13,875.8 | |

$+3\sigma \text{}(\mathrm{Upper}99)$ | 31,796.1 | |

$-3\sigma \text{}(\mathrm{Lower}99)$ | 12,492.6 |

Number | Deck Thickness (mm) | Fatigue Crack Location | Fatigue Life (10^{4}) | Nominal Stress Range (MPa) | Equivalent Structural Stress Range (MPa) |
---|---|---|---|---|---|

OSD1 | 14 | WJ-5 | 27.8 | 200 | 232.05 |

OSD2 | WJ-2 | 93.4 | 150 | 270.49 | |

OSD3 | WJ-3 | 43.7 | 175 | 308.73 | |

OSD5 | 16 | WJ-5 | 23.4 | 200 | 235.59 |

OSD6 | WJ-2 | 151.5 | 150 | 274.32 | |

OSD7 | WJ-5 | 127.0 | 175 | 314.04 | |

OSD9 | 18 | WJ-5 | 35.2 | 200 | 241.17 |

OSD10 | WJ-5 | 136.7 | 150 | 280.34 | |

OSD11 | WJ-5 | 81.6 | 175 | 321.68 |

Time (s) | ${\mathit{\sigma}}_{\mathit{m}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{\sigma}}_{\mathit{b}}\text{}\left(\mathbf{MPa}\right)$ | $\mathit{r}$ | $\mathit{I}{\left(\mathit{r}\right)}^{\frac{1}{\mathit{n}}}$ | ${\mathit{t}}^{\ast}$ | ${\mathit{\sigma}}_{\mathit{s}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{S}}_{\mathit{s}}\text{}\left(\mathbf{MPa}\right)$ |
---|---|---|---|---|---|---|---|

0.56 | −0.49 | −20.39 | 0.98 | 1.32 | 12 | −20.88 | −27.39 |

0.77 | −1.05 | −44.73 | 0.98 | 1.32 | 12 | −45.78 | −60.03 |

1.19 | −0.94 | −40.25 | 0.98 | 1.32 | 12 | −41.19 | −54.02 |

1.27 | −0.95 | −40.79 | 0.98 | 1.32 | 12 | −41.74 | −54.74 |

Approach | Equation No. | Step | ||||||
---|---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | ||||

Stress Time History Curve | $\mathbf{\Delta}{\mathit{S}}_{\mathit{e}\mathit{q}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{n}}_{\mathit{e}\mathit{q}}$ | $\mathit{N}$$\text{}(\times {10}^{7})$ | ${\mathit{D}}_{4}$ | ${\mathit{D}}_{\mathit{T}}$ | ${\mathit{N}}_{\mathit{a}}\text{}\left(\mathbf{years}\right)$ | ||

Extrapolated hot spot stress | $\mathrm{Equation}\text{}\left(15\right)\text{}{m}_{1}=3,\text{}{m}_{2}=5$ | Figure 17 | 40.25 | 4 | 6.4852 | 0.0099 | 0.0121 | 83 |

Stress integration | $\mathrm{Equation}\text{}\left(13\right)\text{}{m}_{1}=3.125,\text{}{m}_{2}=5$ | Figure 17 | 54.89 | 4 | 6.5136 | 0.0098 | 0.0119 | 84 |

$\mathrm{Equation}\text{}\left(14\right)\text{}{m}_{1}={m}_{2}=3.125$ | Figure 17 | 54.89 | 4 | 3.2258 | 0.0194 | 0.0303 | 33 |

Weld no. | L_{1} | L_{2} | L_{3} | Weld no. | L_{1} | L_{2} | L_{3} |
---|---|---|---|---|---|---|---|

1 | 10.9 | 11.4 | 17.5 | 20 | 5.4 | 7.1 | 10.0 |

2 | 7.4 | 12.2 | 15.8 | 21 | 10.7 | 7.8 | 14.3 |

3 | 9.6 | 12.0 | 16.8 | 22 | 9.9 | 6.3 | 12.9 |

4 | 8.7 | 10.4 | 15.0 | 23 | 10.2 | 9.5 | 15.1 |

5 | 8.6 | 9.4 | 13.9 | 24 | 8.4 | 7.9 | 12.6 |

6 | 8.7 | 16.2 | 20.0 | 25 | 6.9 | 9.3 | 12.4 |

7 | 9.5 | 10.5 | 15.4 | 26 | 12.4 | 12.1 | 18.9 |

8 | 10.4 | 10.5 | 16.0 | 27 | 10.4 | 10.9 | 16.3 |

9 | 8.9 | 11.7 | 15.9 | 28 | 8.2 | 13.6 | 17.6 |

10 | 10.6 | 9.8 | 15.9 | 29 | 9.8 | 10.7 | 15.6 |

11 | 11.6 | 12.4 | 18.8 | 30 | 9.8 | 8.8 | 14.5 |

12 | 12.7 | 11.8 | 19.2 | 31 | 9.7 | 11.0 | 15.9 |

13 | 11.6 | 12.4 | 18.7 | 32 | 8.9 | 9.8 | 14.2 |

14 | 10.3 | 11.2 | 16.7 | 33 | 11.0 | 11.8 | 17.5 |

15 | 7.2 | 8.7 | 12.5 | 34 | 10.4 | 15.0 | 19.8 |

16 | 8.8 | 7.6 | 12.8 | 35 | 10.9 | 11.1 | 17.0 |

17 | 7.9 | 12.1 | 15.9 | 36 | 10.7 | 10.8 | 16.4 |

18 | 10.0 | 7.8 | 13.8 | 37 | 10.8 | 10.7 | 15.8 |

19 | 9.4 | 7.1 | 13.0 | 38 | 10.5 | 9.6 | 15.6 |

Statistics Value | ${\mathit{L}}_{1}\text{}\left(\mathbf{mm}\right)$ | ${\mathit{L}}_{2}\text{}\left(\mathbf{mm}\right)$ | ${\mathit{L}}_{3}\text{}\left(\mathbf{mm}\right)$ | ${\mathit{\alpha}}_{1}\text{}(\xb0)$ | ${\mathit{\alpha}}_{2}\text{}(\xb0)$ | ${\mathit{\alpha}}_{3}\text{}(\xb0)$ |
---|---|---|---|---|---|---|

Mean | 9.68 | 10.5 | 15.68 | 37.14 | 40.92 | 101.94 |

Minimum | 5.4 | 6.3 | 10 | 25.11 | 28.38 | 94.59 |

Maximum | 12.7 | 16.2 | 20 | 48.32 | 52.21 | 105.45 |

Weld Types | ${\mathit{\alpha}}_{1}$ | ${\mathit{\alpha}}_{2}$ | ${\mathit{\alpha}}_{3}$ | L1 | L2 | L3 | Area |
---|---|---|---|---|---|---|---|

WT-1 | 30 | 50 | 100 | 5.2 | 8 | 10.28 | 20.57 |

WT-2 | 40 | 40 | 100 | 8 | 8 | 12.26 | 31.51 |

WT-3 | 50 | 30 | 100 | 12.3 | 8 | 15.76 | 48.28 |

WT-4 | 40 | 40 | 100 | 10 | 10 | 15.32 | 49.24 |

WT-5 | 40 | 40 | 100 | 12.5 | 12.5 | 19.15 | 76.94 |

Grinding Type | $\mathit{r}$ (mm) | $\mathit{d}$ (mm) | $\mathit{\phi}$$\text{}(\circ )$ | ${\mathit{S}}_{\mathit{s}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{N}}_{\mathit{a}}\text{}\left(\mathbf{years}\right)$ |
---|---|---|---|---|---|

Non-grinding | — | — | — | 55.35 | 84 |

GT1 | 3 | 0.5 | 70 | 58.53 | 63 |

GT2 | 3 | 0 | 50 | 54.31 | 92 |

Penetration Rate | ${\mathit{\sigma}}_{\mathit{s}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{S}}_{\mathit{s}}\text{}\left(\mathbf{MPa}\right)$ | ${\mathit{N}}_{\mathit{a}}\text{}\left(\mathbf{Years}\right)$ |
---|---|---|---|

80% | 41.67 | 54.64 | 89 |

100% | 42.21 | 55.35 | 84 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cao, B.; Ding, Y.; Fang, Z.; Geng, F.; Song, Y.
Influence of Weld Parameters on the Fatigue Life of Deck-Rib Welding Details in Orthotropic Steel Decks Based on the Improved Stress Integration Approach. *Appl. Sci.* **2019**, *9*, 3917.
https://doi.org/10.3390/app9183917

**AMA Style**

Cao B, Ding Y, Fang Z, Geng F, Song Y.
Influence of Weld Parameters on the Fatigue Life of Deck-Rib Welding Details in Orthotropic Steel Decks Based on the Improved Stress Integration Approach. *Applied Sciences*. 2019; 9(18):3917.
https://doi.org/10.3390/app9183917

**Chicago/Turabian Style**

Cao, Baoya, Youliang Ding, Zhao Fang, Fangfang Geng, and Yongsheng Song.
2019. "Influence of Weld Parameters on the Fatigue Life of Deck-Rib Welding Details in Orthotropic Steel Decks Based on the Improved Stress Integration Approach" *Applied Sciences* 9, no. 18: 3917.
https://doi.org/10.3390/app9183917